Integer Geometry refers to the Geometry on R^n with congruency defined by SL(2,Z) transformations --- this means that if there is a skew, rotation, reflection or other affine transformation between two objects that maps one object to another, they are "integer congruent". For those studying integer geometry, we consider these objects to be the same. In particular, those who study this geometry are generally interested in objects with vertices in Z^n. Common objects to study are integer angles (and in higher dimensions, simplicial cones), integer polygons and integer circles.

We define the integer length of a segment AB to be one fewer than the number of integer points (that is, points on the lattice Z^2) contained within the segment AB including its endpoints. The integer distance between two points is equal to the length of the segment between them --- note that this is not a distance in terms of metric spaces as it fails the triangle inequality.

The integer distance between a point and a line is one less than the number of parallel integer lines between the point and the line, including the line itself and the line passing through the point.

Research into integer geometry is carried out by many mathematicians, including:

Oleg Karpenkov,

Matty Van Son,

John Blackman,

Rebecca Sheppard,

Anna Pratoussevich.

Last change to this page
Full Page history
Links to this page
 Edit this page
  (with sufficient authority)
Change password
 Recent changes
All pages
Search